
Next, the minimizer of the corresponding (strictly) convex linear functional \(J_n(\phi )\)  appearing in Step 4 of algorithm 1 can be found by solving the corresponding Normal equation. For brevity, we do not describe the finite difference implementation of various operators appearing in the expression for the Normal equation corresponding to \(J_n(\phi )\)  as these are similar to those discussed elsewhere, see e.g. [1]}.
We briefly mention that the matrix forms of all such operators is necessarily stored as sparse matrices. Solution to this Normal equation is then found by using the MATLAB function `lsqlin' which in turn is the
minimizer of the functional \(J_n(\phi )\)  on \(H_0\) . 
We let the iterative Algorithm 1 run for six iterations, i.e. \(n=6\)  as it was observed that \(\Vert U_{6} - U_{5}\Vert _{L^{\infty }}\)  was small enough in all numerical experiments.
